Formal, Informal Or Anti-Logical? the Philosophy of the Logician Evert Willem Beth (1908-1964)

INFORMAL LOGIC XII. 1, Winter 1990 In the Service of Human Society: Formal, Informal or Anti-Logical? The Philosophy of the Logician Evert Willem Beth (1908-1964) E. M. BARTH Groningen University Introduction 1. Where does European argumentation theory come from? Proof as a social act The topic on which I have been asked to speak is, as far as I understood it, the Where does the highly amorphous field formal-informal divide in logic. Having called argumentation theory derive from? pondered about that task for a long time I There is, I believe, a certain difference be decided that concerning a weighing of the tween the United States on the one hand and pro's and con's of the two approaches I Europe and Canada on the other in this want to cut it short and to simply say: respect. Whereas in the United States the There ought to be formal logic, attuned departments of speech communication seem to human affairs; to have been very influential indeed, in There ought to be informal logic, attuned Europe argumentation theory derives from to human affairs; philosophy, and to a very large extent from logic-as in Canada. and once upon a time the twain shall meet. This fact is of considerable importance I do not accept the formal-informal for an understanding of the possibilities of, divide as a divide. That distinction ought and in, the field, as I shall try to show. Five to be played down. It is merely a question European philosophers at least from the of method-an interesting question, but not generation before us must be mentioned, at all a threatening one. A plurality or without whom this field would hardly have richness of methods is something to rejoice in. existed in Europe. They are, in Second, I have noticed a not unsurpris chronological order of the onset of their ing lack of understanding of the origins of work, Arne Naess of Norway, Chaim argumentation theory, especially in so far Perelman and Lucie Olbrechts-Tyteca of as these are European origins. I believe that Belgium, Evert Willem Beth of the a better understanding of those origins may Netherlands, Paul Lorenzen of the German contribute to a lessening of tensions caus Federal Republic. One of the logicians in ed by the formal-informal divide. question, Arne Naess, has used informal I shall try to work on your ideas by way methods-which made the Wiener Kreis of feeding your fantasy rather than by argu philosophers unwilling to take his 1936 ing. I'll supply you with a case history about "discussion calculus" seriously. Beth and one human being, the Dutch logician Lorenzen are formal logicians. I want to philosopher Evert Willem Beth, who was show that this last difference is less impor born in 1908 and died in 1964. His tant than some hold it to be-much less dialogically oriented philosophy happens to important. be one of the basic sources of argumentation To start with, what these two formal theory in Europe. I shall not discuss tech logicians, Beth and Lorenzen, have done nical details but concentrate on his outlook is certainly not triviaL I can prove-in an on logic and the needs of humanity. I do indirect manner, by means of a couple of that, however, by means of a short detour. case histories-that it is not. In 1977 the 2 E. M. Barth logician Yu. I. Manin published (an English that moment, in 1951, Church was editor version ot) his textbook on the intimidating in-chief of the Journal of Symbolic Logic subject of mathematical logic, this belov (the JSL). Beth was a member of its editorial ed play-pen of autistic academics (my judge board and had been so since shortly before ment, not his). The book contained one par World War II. On 11 June 1951 Beth writes ticularly remarkable section, so unusual that to the then editor-in-chief of the JSL, Alon a couple of years later the journal The zo Church, to tell him that he is very disap Mathematical Intelligencer published it. pointed in a review that Church had sent Manin's "provocative digression on him in manuscript for his information, of proof", as The Mathemtical Intelligencer his own book Fondements de Logique, writ called it, turns out to be the following ten in French. The review, intended for the philosophical statement: JSL, is not yet printed and Beth asks Church It A proof only becomes a proof after the to request the reviewer to revise it. is a social act of "accepting it as a proof'. This very negative review that points out a is as true for mathematics as it is for physics, number of technical inaccuracies and linguistics, or biology. The evolution of mistakes in Beth's book; and this is the on commonly accepted criteria for an argu ly aspect of the book to which the reviewer ment's being a proof is an almost untouch has paid any attention at all. Beth regards ed theme in the history of science. I this as extremely unfair, considering what Then the act of "proving", too, is a social he himself sees as the general aim of the act. book. He also (correctly) is of the opinion This is what the editors of the journal that a number of the mistakes or errors the The Mathematical Intelligencer found pro reviewer refers to hardly can be characteriz vocative. Manin's statement was, of course, ed as errors at all. He writes: very much in line with the spirit of the I do not question the competence of Miss dialogical form oflogic, whether formal or Novak [the reviewer]. Nor do I fail to informal. 2 recognize that, to my regret, my In the same issue of The Mathematical "Fondements" contains a number of errors. Intelligencer, the editors had invited two I feel however-and this feeling seems to be other mathematical logicians (in the nar shared by other reviewers-that these errors, most of them being minor slips, do not rower sense) to participate in a discussion seriously detract from the intrinsic value of about this thesis and the rest of the reprinted the book. Therefore I think that a review section. One of them was Solomon Fefer which restricts itself to listing some of these man from Stanford University. However, errors and adds a number of would-be in his answer to Manin, Feferman does not mistakes, cannot do justice to my book. discuss a single one of Manin's remarks. Church answers with a letter of 22 June, saying that he personally accepts the review and will publish it. He writes: 2. Logic and cultural politics I believe that the explanation must be that your book was written hastily, under If the Manin-Feferman verbal exchange pressure ofthe many other obligations that can be called a discussion, then Feferman I know you have undertaken, and that you has lost it, for he does not deal with the simply failed to take the care and make the thesis in question. I would like to compare many detailed checks which a work of this this discussion (if it is one) with one that sort demands ... .I do regret, when books of took place twenty -eight years earlier, be a low quality in matters of logic are being written, the necessity of publishing an un tween the Dutch logician-philosopher Evert favorable review of an author [Beth] of real Willem Beth3 and the American Alonzo standing in our field. But you must realize Church, of the undecidability theorem. At that this consideration has another Beth as Logician 3 side. [Certain authors of books on logic, In another letter, addressed to S. C. among which is the psychologist Piaget] may Kleene, Beth writes: deceive the outsider, but not the serious stu dent of modern logic. The Journal is after I am completely at a loss as to the motives all addressed primarily to logicians, and it behind Church's action or the lack of such is precisely the errors of recognized logi motives (italics mine). cians which it is most important to correct 'Or the lack of such motives': this seem if our Reviews section is to perfonn its func tion (italics mine). ingly fortuitous, casual remark is in my opi nion the pivot on which the Beth-Church In his reply of June 30, Beth starts by discussion hinges. Church was not inspired saying that he appreciates the frankness of by the goals and ideals that inspired Beth. Church's letter. This new letter of Beth's Beth looked in vain for signs of the same runs to three full typed pages. The second motivation in others, suspected a gap where half of this letter is of general logico he himself was a sea of fire and purposeful philosophical interest. Beth now writes: elan, and was in this respect indeed a loner among his colleagues. As these words and It seems to me that your outlook on the situa the discussion in which they were uttered tion as a whole is entirely mistaken and that, no less than the reviewer, [you] fail to probably make clear Beth was-like Manin, realize the fact that the book was written for though without publishing any explicit state French readers. Since 1940, the following ment to that-inspired by a semiotical two books have been published in France (here role philosophy which he very consistent five names of authors follow). I do not think ly put into practice. Thus one writes that my book, in spite of a number of regret something, or proves something, for table mistakes, is worse than any of them.

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